Solved – Stata multinomial logit IIA assumption violated or not

hausmanmlogitmultinomial logitstata

My dependent variable is Choice, 0 for non-issuers, 1 for seasoned equity issuers, 2 for convertible issuers and 3 for bond issuers.
I use the following command to run a multinomial logit regression:

mlogit Choice CR $ConVar, base(0)

To test for IIA assumption, I use the following command:

mlogtest, haus

The output is below:

Does this result indicate that IIA is violated?

Then I test the IIA assumption for another multinomial logit regression, in which the dependent variable is Security (0 for seasoned equity issuers, 1 for convertible issuers, and 2 for bond issuers).
The Stata commands are below:

mlogit Security CR $ConVar, base(0)
mlogtest, haus

Output of IIA test is shown below:

Again, does this mean that the IIA assumption is violated?

Could anyone interpret these two results for me? And I am not sure why some categories of dependent variables have negative chi2.

Best Answer

Significant values of chi2 indicate that the IIA assumption has been violated. You can look at the p-values in the 4th column to gauge that.

Some of your test statistics are negative, which is fairly common. Hausman and McFadden (1984, p. 1226) argue that a negative result is evidence that IIA has not been violated.

This logic would suggest that the first one passes, and the second fails.

A good, accessible book with lots of Stata examples and much intuition on this is Long & Freese's Regression Models for Categorical Dependent Variables Using Stata.

The (partially gated) paper mentioned above is: Hausman, Jerry, and Daniel McFadden. "Specification Tests for the Multinomial Logit Model." Econometrica 52, no. 5 (1984): 1219-240.

Related Solutions

Solved – Multinomial Logistic Regression: IIA violated – What to do

Depending on your version of Stata, you can try the new syntax for hausman:

webuse sysdsn1
mlogit insure age male 
estimates store Full
mlogit insure age male if insure !="Uninsure":insure
estimates store Restricted
hausman Restricted Full, alleqs constant

I can't get mlogtest to work with Stata 13 (it's an older, user-written command), so I can't verify it's the same error, but here's an example of a Hausman test that fails:

mlogit insure age male if insure !="Prepaid":insure
hausman Restricted Full, alleqs constant

The test involved calculating the test statistic $H = (b-B)'V(b-B)^{-1}(b-B)$. The problem has to do with the estimator of the variance $V(b-B)$ as $V(b)-V(B)$, which is only asymptotically feasible. $b$ and $B$ are the restricted and unrestricted coefficient vectors. Here it isn't a proper variance matrix, and the Hausman test becomes undefined.

suest estimates the simultaneous variance-covariance of the coefficients, and you can use it in the following way:

suest Restricted Full, noomitted
test [Restricted_Uninsure = Full_Uninsure], cons

suest estimates $V(b-B)$ by $V(b)-Cov(b,B)-Cov(B,b)+V(B)$. This is always admissible, so the resulting test is always well defined. I would prefer this.

You will have to loop over dropped categories to get all the tests.

@marquisdecarabas Something like this:

webuse sysdsn1
mlogit insure age male 
estimates store m1, title("Full Model")
mlogit insure age male if insure != "Uninsure":insure
estimates store m2, title("Not Uninsured")
mlogit insure age male if insure != "Prepaid":insure
estimates store m3, title("Not Prepaid")

suest m1 m2 m3, noomitted
test [m1_Prepaid = m2_Prepaid], cons
test [m1_Uninsure = m3_Uninsure], cons accum

Solved – IIA assumption: difference logit and probit

A violation of the IIA assumption is basically a case of correlation between the residuals for the equations predicting each of the $k-1$ categories (excluding the baseline) of the response variable. A classic example is when you have two similar modes of transport like a blue bus and a red bus: people unmeasured characteristics that make them more likely to choose blue bus may also make them likely to choose red bus because both are similar alternatives (e.g. maybe among the unmeasured characteristics is a preference for public transportation that affects both blue and red bus choice).

Multinomial logit and independent multinomial probit assume IIA because they assume that the residuals in each equation are uncorrelated. Nested logit and probit partially relax this assumption by dividing alternatives into subsets that are similar among themselves (e.g. placing red and blue bus within a subset of public transportation) but independent from the ones in the other subsets. Multilevel multinomial logit tries to deal with IIA by modelling the unobservable component: IIA is not an issue if the correlated unobservable heterogeneity is accounted for by the model. Mixed logit deals with IIA by allowing coefficients to vary between decision-makers, reflecting individual observed differences in preferences. Lastly, alternative specific multinomial probit models the full correlation matrix of the residuals, allowing for them to be correlated and doing away with IIA completely.

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Related Solutions

Solved – Multinomial Logistic Regression: IIA violated – What to do

Solved – IIA assumption: difference logit and probit

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